{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3UDG532XFJMXXY7JY6SR4OTQDH","short_pith_number":"pith:3UDG532X","schema_version":"1.0","canonical_sha256":"dd066eef572a597be3e9c7a51e3a7019e5f79977c1aef01803c52d4c9bfb7061","source":{"kind":"arxiv","id":"1203.1991","version":3},"attestation_state":"computed","paper":{"title":"Periodic Occurance of Complete Intersection Monomial Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"A. V. Jayanthan, Hema Srinivasan","submitted_at":"2012-03-09T04:49:37Z","abstract_excerpt":"We study the complete intersection property of monomial curves in the family $\\Gamma_{\\aa + \\jj} = {(t^{a_0 + j}, t^{a_1+j},..., t^{a_n + j}) ~ | ~ j \\geq 0, ~ a_0 < a_1 <...< a_n}$. We prove that if $\\Gamma_{\\aa+\\jj}$ is a complete intersection for $j \\gg0$, then $\\Gamma_{\\aa+\\jj+\\underline{a_n}}$ is a complete intersection for $j \\gg 0$. This proves a conjecture of Herzog and Srinivasan on eventual periodicity of Betti numbers of semigroup rings under translations for complete intersections. We also show that if $\\Gamma_{\\aa+\\jj}$ is a complete intersection for $j \\gg 0$, then $\\Gamma_{\\aa}$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1203.1991","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-03-09T04:49:37Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8715c36b2ca588eab3d824ef37e96669318c41fa18b7f25d4a0c2b7bd00004c4","abstract_canon_sha256":"b336c3db2d688810eeee6157eefde7146eb8717dd2b6e5c6ca0546f49fdfc9d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:48.936770Z","signature_b64":"l9vGAE0YUoCj0RKcxayEbDskByTCvVvEkXcfWWuUiA5KbuesmVo1ih4BM70AQSbF8xi1AsKDpgtf9gsrIFTdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd066eef572a597be3e9c7a51e3a7019e5f79977c1aef01803c52d4c9bfb7061","last_reissued_at":"2026-05-18T03:59:48.936134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:48.936134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Periodic Occurance of Complete Intersection Monomial Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"A. V. Jayanthan, Hema Srinivasan","submitted_at":"2012-03-09T04:49:37Z","abstract_excerpt":"We study the complete intersection property of monomial curves in the family $\\Gamma_{\\aa + \\jj} = {(t^{a_0 + j}, t^{a_1+j},..., t^{a_n + j}) ~ | ~ j \\geq 0, ~ a_0 < a_1 <...< a_n}$. We prove that if $\\Gamma_{\\aa+\\jj}$ is a complete intersection for $j \\gg0$, then $\\Gamma_{\\aa+\\jj+\\underline{a_n}}$ is a complete intersection for $j \\gg 0$. This proves a conjecture of Herzog and Srinivasan on eventual periodicity of Betti numbers of semigroup rings under translations for complete intersections. We also show that if $\\Gamma_{\\aa+\\jj}$ is a complete intersection for $j \\gg 0$, then $\\Gamma_{\\aa}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1991","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1203.1991","created_at":"2026-05-18T03:59:48.936225+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.1991v3","created_at":"2026-05-18T03:59:48.936225+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1991","created_at":"2026-05-18T03:59:48.936225+00:00"},{"alias_kind":"pith_short_12","alias_value":"3UDG532XFJMX","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3UDG532XFJMXXY7J","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3UDG532X","created_at":"2026-05-18T12:26:53.410803+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3UDG532XFJMXXY7JY6SR4OTQDH","json":"https://pith.science/pith/3UDG532XFJMXXY7JY6SR4OTQDH.json","graph_json":"https://pith.science/api/pith-number/3UDG532XFJMXXY7JY6SR4OTQDH/graph.json","events_json":"https://pith.science/api/pith-number/3UDG532XFJMXXY7JY6SR4OTQDH/events.json","paper":"https://pith.science/paper/3UDG532X"},"agent_actions":{"view_html":"https://pith.science/pith/3UDG532XFJMXXY7JY6SR4OTQDH","download_json":"https://pith.science/pith/3UDG532XFJMXXY7JY6SR4OTQDH.json","view_paper":"https://pith.science/paper/3UDG532X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.1991&json=true","fetch_graph":"https://pith.science/api/pith-number/3UDG532XFJMXXY7JY6SR4OTQDH/graph.json","fetch_events":"https://pith.science/api/pith-number/3UDG532XFJMXXY7JY6SR4OTQDH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3UDG532XFJMXXY7JY6SR4OTQDH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3UDG532XFJMXXY7JY6SR4OTQDH/action/storage_attestation","attest_author":"https://pith.science/pith/3UDG532XFJMXXY7JY6SR4OTQDH/action/author_attestation","sign_citation":"https://pith.science/pith/3UDG532XFJMXXY7JY6SR4OTQDH/action/citation_signature","submit_replication":"https://pith.science/pith/3UDG532XFJMXXY7JY6SR4OTQDH/action/replication_record"}},"created_at":"2026-05-18T03:59:48.936225+00:00","updated_at":"2026-05-18T03:59:48.936225+00:00"}